root-mean-square speed
The molecules in a gas do not all move at the same speed — some dawdle, some race, most are somewhere in between. If you want a single number to stand for how fast they typically go, the root-mean-square speed is the kind of average that the physics naturally hands you.
Its name spells out the recipe in reverse: take each molecule's speed, square it, average those squares over all the molecules, then take the square root. This particular average is special because the squared speed is what determines kinetic energy, so the rms speed connects directly to the temperature: it grows with the square root of the absolute temperature and shrinks with the square root of the molecule's mass.
It matters because it gives a concrete feel for molecular motion — at room temperature ordinary air molecules whiz along at hundreds of metres per second, faster than a jet plane. It also explains why light gases like hydrogen and helium move so much faster than heavy ones, the fact behind effusion rates and even why our atmosphere keeps oxygen but leaks helium to space.
At room temperature the rms speed of nitrogen molecules in the air around you is roughly 500 metres per second — over a thousand miles per hour — yet they travel only a tiny distance between collisions, so the air feels perfectly still.
Air molecules race at hundreds of metres per second even in a still room.
The rms speed is slightly higher than both the average (mean) speed and the most probable speed, because squaring gives extra weight to the fastest molecules. The three are close but not identical, and it is worth knowing which one a formula calls for.